Upon arriving at the 15 DME fix on a heading of 350°, which holding pattern complies with the ATC instruction for the specified clearance?

The correct option involves holding patterns defined by their entry methods and the orientation of the aircraft as it arrives at the holding fix. When using a direct entry method to a holding pattern, the aircraft approaches the fix straight on, and upon arrival there, it makes a turn in the appropriate direction to enter the pattern.

Upon arriving at the 15 DME fix on a heading of 350°, the flight is positioned to execute a direct entry into the holding pattern, which means that once the aircraft reaches the fix, it can make an immediate turn to the right (or left, depending on the published instructions) to join the holding pattern. This is compliant with standard holding procedures as the aircraft is already aligned with the entry path.

This scenario reflects the procedural compliance with ATC instructions and reinforces the importance of understanding the various entry methods into holding patterns, particularly that direct entries are used when the aircraft is approaching the holding fix on a bearing that aligns well with the holding course. This makes option C the most suitable choice given the circumstances described.